I've met a few people who moved across continents in their youth, sometimes multiple times. Almost without a fault, they are somewhat obsessed with the concept of 'home'.

My longest time abroad was a year in Chicago, and the place where I grew up is far too boring to ever be considered 'home', so I really have no idea where 'home' would be for me. But I'm largely just indifferent to the idea.

FWIW: I have many American friends living here in Berlin, and none of them are really struggling with their identity. But it may be different if you never had the experience of being part of the 'native' population... It's probably a similar fate to what members of other minorities (religion/race/disability) experience.